tag:blogger.com,1999:blog-264226589944705290.post8469577593411191964..comments2023-06-03T04:58:32.301-07:00Comments on God Plays Dice: Optimal choice of partnersMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-264226589944705290.post-29310113902934880282009-03-08T18:25:00.000-07:002009-03-08T18:25:00.000-07:00Thanks for the info, you can also find Government ...Thanks for the info, you can also find <A HREF="http://www.governmentfreegrants.org" REL="nofollow">Government Grants</A> here,<BR/>or <A HREF="http://www.governmentfreegrants.org/free-government-grant-kit/" REL="nofollow">Free Grant Kit</A> here,<BR/><A HREF="http://www.governmentfreegrants.org/government-grants/how-to-get-free-grant-kit/" REL="nofollow">Free Grant Kit</A> Grant KitAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-47577272365675553452008-11-10T11:18:00.000-08:002008-11-10T11:18:00.000-08:00Good post.Good post.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-14360238164396317722008-08-31T01:04:00.000-07:002008-08-31T01:04:00.000-07:00I have heard that there are government grants avai...I have heard that there are government grants available to help women and minorities with a small business. Finding the actual grants is a little difficult any information the actual name of the specific grants or something to send me in the right direction would help. Anyone have info on obtaining a government grant for small businesses? Thanks.<BR/><BR/><BR/>Sudipta Das<BR/>______________<BR/><BR/><A HREF="http://www.governmentgrantauthority.com" REL="nofollow">Free grant</A>Sudipta Dashttps://www.blogger.com/profile/15576598115739268572noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-77879286775951486602008-05-23T15:34:00.000-07:002008-05-23T15:34:00.000-07:00My readers who are mathematicians probably didn't ...<I>My readers who are mathematicians probably didn't read the previous paragraph.</I><BR/><BR/>Ha ha, maybe, but I found the discussion of the assumptions as interesting as the result itself.Alexhttps://www.blogger.com/profile/07509233273590036699noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-81979433973907467072008-05-19T09:04:00.000-07:002008-05-19T09:04:00.000-07:00unapologetic: Good catch. The odds of that situati...unapologetic: Good catch. The odds of that situation would be 1/16, if I've figured it correctly. (1/8 chance that each card in the correct half, and 1/2 for the required ordering of the cards in the second half.) Then you can continue figuring the probabilities for 4 cards, 5 cards, etc. The total probability would be 1/4 + 1/16 + 1/64 + 1/256... which I believe converges on 1/3 -- noticeably better than 1/4!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-89576060633913166802008-05-19T09:02:00.000-07:002008-05-19T09:02:00.000-07:00My readers who are mathematicians probably didn't ...<I>My readers who are mathematicians probably didn't read the previous paragraph.</I><BR/><BR/>Heh. I'm laughing at myself right now for being predictable.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-38889563394861580202008-05-18T18:41:00.000-07:002008-05-18T18:41:00.000-07:00There is an elegant proof in Mosteller's "Fifty Ch...There is an elegant proof in Mosteller's "Fifty Challenging Problems in Probablity." See problem # 47, "Choosing the largest Dowry."<BR/><BR/>There is also a large literature on optimal stopping problemsAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-15898406007659603892008-05-18T18:05:00.000-07:002008-05-18T18:05:00.000-07:00susan, what about if the third-highest is in the f...susan, what about if the third-highest is in the first half of the deck, the first and second are both in the second half, and the second comes after the first. Then you'll also win, won't you?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-58243399495836853612008-05-18T16:00:00.000-07:002008-05-18T16:00:00.000-07:00I agree with the connection to derangements. And ...I agree with the connection to derangements. And of course this is a problem about a property of permutations. There might be a connection; I haven't thought about it.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-37400083755526726432008-05-18T14:43:00.000-07:002008-05-18T14:43:00.000-07:00I first heard this problem in the context of a gam...I first heard this problem in the context of a game. You have a stack of a million index cards which you'll go through one by one, and you have to stop when you think you're on the highest card. I find this version a little easier to picture, since the assumptions you listed are much easier to control.<BR/><BR/>A good first pass at the strategy is what you described, except rejecting the first half of the cards (instead of 1/e). This is not optimal, but still surprisingly good--for large N, you have a 1/4 chance of winning, and it's easier to prove than the optimal solution. Basically, you'll win if and only if the highest card is in the second half and the second-highest card is in the first half, and this will obviously occur about 1/4 of the time.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-64967806668414273642008-05-18T13:44:00.000-07:002008-05-18T13:44:00.000-07:00Do we really want to maximize our probability of f...Do we really want to maximize our probability of finding the best one? This strategy of course guarantees that if you meet the best one in the first 1/e of your dating life, you'll remain unwed forever, despite finding people who come very close in quality to that high point. I think a slightly more forgiving strategy would be better, but then we need not just "X > Y" but an actual numerical value for each suitor.Joshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-65800827864217873762008-05-18T11:56:00.000-07:002008-05-18T11:56:00.000-07:00The fourth assumption, that you know how many pote...<I>The fourth assumption, that you know how many potential suitors there are, seems the most wrong to me.</I><BR/><BR/>That's exactly why I hated this formulation. It's a great toy problem, but horrible marketing. Besides, it gives the lay audience the impression that we mathematicians actually think so coldly and calculatingly about romance.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-87520946774028833672008-05-18T11:37:00.000-07:002008-05-18T11:37:00.000-07:00That "1/e for large N" reminds one immediately of ...That "1/e for large N" reminds one immediately of counting the number of derangements! I wonder if there is some connection there.Anonymousnoreply@blogger.com